To solve this inequality, we can start by multiplying both sides by (1-х) to clear the denominator:
(1/5)^(2х+1) > 125(1-х)
Next, we can rewrite 125 as 5^3 because 5^3 = 125:
(1/5)^(2х+1) > 5^3(1-х)
Now, we can simplify the right side:
(1/5)^(2х+1) > 5^(3)(1-х) (1/5)^(2х+1) > 5^(3) - 5^(4)х (1/5)^(2х+1) > 125 - 625х
Now, we can rewrite the left side using the property that (a^b)^c = a^(b*c):
5^(-2х-1) > 125 - 625х
Now, we have a simpler form of the inequality. We can then rearrange it to isolate the terms with x on one side:
1/5^(2х+1) > 125 - 625х 5^(2х+1) < 1/(125 - 625х) 5^(2х+1) < 1/(125(1 - 5х))
At this point, we can see that it's a bit tricky because of the logarithms. To further simplify or solve for x, we may need to use logarithms or a numerical method. Let me know if you want to proceed in that direction.
To solve this inequality, we can start by multiplying both sides by (1-х) to clear the denominator:
(1/5)^(2х+1) > 125(1-х)
Next, we can rewrite 125 as 5^3 because 5^3 = 125:
(1/5)^(2х+1) > 5^3(1-х)
Now, we can simplify the right side:
(1/5)^(2х+1) > 5^(3)(1-х)
(1/5)^(2х+1) > 5^(3) - 5^(4)х
(1/5)^(2х+1) > 125 - 625х
Now, we can rewrite the left side using the property that (a^b)^c = a^(b*c):
5^(-2х-1) > 125 - 625х
Now, we have a simpler form of the inequality. We can then rearrange it to isolate the terms with x on one side:
1/5^(2х+1) > 125 - 625х
5^(2х+1) < 1/(125 - 625х)
5^(2х+1) < 1/(125(1 - 5х))
At this point, we can see that it's a bit tricky because of the logarithms. To further simplify or solve for x, we may need to use logarithms or a numerical method. Let me know if you want to proceed in that direction.